**Eugène Catalan** was a Belgian mathematician who defined the numbers called after him, while considering the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals.

- Catalan was therefore born in France, and so rightly considered himself French.
- His name was registered on his birth certificate as Eugène Charles Bardin.
- In May 1822, Joseph and Jeanne Catalan were living in Lille with their son.
- Eugène certainly had had some education and was able to write excellent French by the age of ten.
- Eugène rapidly fell in love with the city and his parents allowed him to roam the streets.
- Although he was only twelve years old at the time, Eugène's dislike of the monarchy is clearly and forcibly expressed.
- In addition to attending courses at the École Gratuite de Dessin, Catalan attended courses at the École des Beaux-Arts.
- At the École Gratuite de Dessin, Catalan was taught by Louis Lefébure de Fourcy who had been appointed as an admissions examiner for the École Polytechnique in 1826.
- He encouraged Catalan, who showed an outstanding aptitude for mathematics, to prepare himself to take the admission examinations for the prestigious university.
- Rather than carry on studying, Catalan spent August and September of that year back in Bruges, the first time he had been in that city since he was eleven years old.
- At the École Polytechnique, Catalan attended mathematics courses given by Joseph Liouville and Gabriel Lamé.
- Despite his strong Republican beliefs, Catalan kept out of trouble.
- Catalan had not been singled out for this punishment, for it appears that the whole of his year suffered the same fate.
- During this forced vacation Catalan took the opportunity to become engaged to Charlotte Augustine Renée Perin (known as Eugénie) who was two years his elder.
- She had been born in Lille, where Catalan had spent several years.
- Catalan had to apologise for an "act of subordination" before he was allowed to return to the École Polytechnique in the middle of January 1835.
- Liouville began publication of Journal de Mathématiques Pures et Appliquées in 1836 and a paper by Catalan, Solution d'un problème de Probabilité relatif au jeu de rencontre Ⓣ(Solution of probability problem relating to the game of meeting), was published in the second volume in 1837.
- The second of these contains the 'Catalan numbers' which appears in the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals.
- Four papers by Catalan are published in Volume 4 in 1839: Note sur la Théorie des Nombres Ⓣ(Note on the theory of numbers); Solution nouvelle de cette question: Un polygone étant donné, de combien de manières peut-on le partager en triangles au moyen de diagonales?
- Catalan was keen to return to Paris and he applied for the professorship at the École Gratuite de Dessin which had become vacant on the death of his former professor Jean-Baptiste-Omer Lavit in 1836.
- He suggested that Catalan needed further qualifications, such as the baccalaureate, in order to make a successful career.
- Later that year, Catalan resigned his position at Châlons-sur-Marne and returned to Paris.
- As soon as he had returned to Paris, in addition to these other tasks, Catalan had taken Liouville's advice regarding his baccalaureate, and began studying hard.
- In July 1839 Cauchy invited Catalan and Lejeune Dirichlet to dinner.
- Catalan was, however, still supported by Liouville who proposed him for membership of the Société Philomatique.
- After being unsuccessful in 1839, Catalan was elected to the Society in May 1840 and began publishing articles in the Society's journal.
- He approached Louis Francoeur asking to be tutored in mathematics and Francoeur advised him to approach Catalan.
- This in fact proved fortunate for Catalan since Tchihatchef had been given a paper by the Russian mathematician Pafnuty Chebyshev to submit for publication in Paris.
- Tchihatchef showed Catalan the paper and Catalan began to correspond with Chebyshev; a correspondence which continued for fifty years.
- It was followed in the same journal by a short paper by Catalan proving a formula for the transformation of a multiple integral stated without proof in Chebyshev's paper.
- On 6 January 1844 Catalan was appointed as secretary of the Société Philomatique.
- In November 1844 he was ranked first by the Council for the position of tutor at the École Polytechnique but Ossian Bonnet was appointed to the position and Catalan remained as an assistant tutor.
- He had received another setback in his career in December 1844 when, after Francoeur had indicated that he wanted Catalan as his deputy at the Sorbonne, he had been rejected by the Royal Council.
- In 1846 Catalan competed in the Concours d'agrégation (a contest to become a university teacher) and was placed first.
- Catalan was paying a high price for his strong, publicly expressed Republican views.
- In September 1846 Catalan wrote to Quetelet indicating that he was beginning to regret having remained in Paris instead of following his suggestion to move to Belgium.
- Catalan took a highly active role in the disturbances, leading a band of workers who entered the Hôtel-de-Ville immediately after a group of students from the École Polytechnique.
- This fitted well with Catalan's Republican views and he offered himself for election to the National Assembly.
- Two admission examiners were appointed in 1848 and, although Catalan was on the list of four offered to the Ministry, Charles Hermite and Joseph Serret were appointed with Abel Transon and Pierre Bonnet as their deputies.
- It reported in November and Catalan did not like either the academic changes that were proposed, particularly the considerable reduction in pure mathematics, nor did he like the fact that much more work was to be undertaken by the tutors.
- Catalan was not the only one to leave the École Polytechnique following the report of Le Verrier's commission; Michel Chasles, Joseph Liouville and Charles-François Sturm also immediately resigned in protest.
- This was bad for Catalan who disliked the Bonapartes as much as he disliked kings.
- This was, almost certainly, part of Catalan's strategy to get elected to the Académie des Sciences.
- For example, he published Sur des surfaces dont les rayons de courbure en chaque point sont égaux et de signes contraires Ⓣ(On surfaces whose radii of curvature at each point is equal and opposite) (1855) which looks at the 'Catalan minimal surface' associated with 'Catalan's minimal curve'.
- He also published in Comptes rendus: Note de M Catalan à l'occasion d'un théorème de M Serret Ⓣ(A note by M Catalan about a theorem of M Serret) (1856), Sur le calcul de la latitude par la méthode de M Babinet Ⓣ(On the computation of latitude by the method of M Babinet) (1856), Sur quelques points de la théorie des séries Ⓣ(On some points of the series of theory) (1856), Sur un cas particulier de la formule du binôme Ⓣ(On a special case of the binomial theorem) (1857), and Sur la théorie des développées Ⓣ(On the theory of developments) (1857).
- When Serret was elected in 1860, Catalan was on the list to be considered but was only ranked fourth equal, behind Serret, Bonnet and Puiseux.
- The Academy proposed a question on polyhedra for the 1861 prize and Catalan submitted an entry.
- The polyhedra that Catalan discovered are now called the Catalan solids.
- In 1859 Catalan had tried to persuade the Ministry of Public Instruction to name him as a Professor of Mathematics at one of the lycées in Paris.
- Since Catalan was born in Bruges it might be supposed that he would feel as if he was coming back to his homeland when he took up the position in Liège.
- However, Catalan always considered himself French, having earlier undergone considerable efforts to reinstate his French citizenship.
- The Franco-Prussian war of 1870-71 did not affect neutral Belgium but Catalan, with his great love of France, was greatly saddened by the humiliation of the French by the Prussians.
- Catalan had never respected the Légion d'Honneur which had been created by Napoleon Bonaparte in 1802.
- The Académie des Sciences, however, discussed at length electing Catalan during the 1870s but failed to do so.
- It contains 69 of Catalan's papers starting from Sur les combinaisons avec répétition Ⓣ(On combinations with repetition) (1838) and ending with his paper Démonstration d'une formule de Poisson Ⓣ(Demonstration of a Poisson formula) (February 1867).
- This work contained 299 of Catalan's papers, the last paper being Sur une application du théorème de Bayes, faite par Laplace Ⓣ(On an application of Bayes' theorem made by Laplace) (August 1888).
- The second volume contains Catalan's retirement speech and the third volume also lists Catalan's publications; the list contains 406 items.
- Catalan was elected to the Belgian Académie Royale des Sciences, des Lettres et des Beaux Arts on 15 December 1865.
- The Belgium government honoured Catalan by awarding him the Cross of the Knight of the Order of Léopold in 1879.
- Catalan retired on 1 June 1884, becoming professor emeritus.
- In this portrait, Catalan is proudly wearing the Knight's Cross of the Order of Léopold.
- In 1890 the Belgium government elevated Catalan to an Officer of the Order of Léopold.
- Catalan wrote several texts which were very popular and many ran into several editions.
- Catalan, one of the oldest living former pupils, planned a final visit to Paris to take part in the celebrations.
- His wife, Eugénie, died on 11 February and Catalan himself died three days later.

Born 30 May 1814, Bruges, French Empire (now Belgium). Died 14 February 1894, Liège, Belgium.

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Astronomy, Origin Belgium, Number Theory, Special Numbers And Numerals

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive